Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
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—Aldous Huxley (1894–1963)
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There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)
“Don: Why are they closed? They’re all closed, every one of them.
Pawnbroker: Sure they are. It’s Yom Kippur.
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—John Locke (1632–1704)